Restricted homotopies and focal conic textures

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Abstract
The effects of integrability conditions on the homotopic defect classification of layered systems are investigated. It is shown, that for irrotational vector fields in three dimensions point defects of any index can be realized. Continuous transitions between defects of the same index are, however, impeded. The circular defect lines of focal conic textures are a manifestation of such a restricted homotopy